Using pseudotime solution framework in harmonic balance methods for aperiodic problems

AIAA Journal

Volumn 51, Issue 12, 2013, Pages 2982-2987

  Attar, Peter J ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE COMMUNITY; APERIODIC RESPONSE; HARMONIC BALANCE METHOD; NONLINEAR ALGEBRAIC EQUATIONS; PSEUDOTRANSIENT CONTINUATION; QUASI-PERIODIC; STEADY STATE SOLUTION; THREE-DIMENSIONAL PROBLEMS;

ALGEBRA; FOURIER SERIES; PLATES (STRUCTURAL COMPONENTS); THREE DIMENSIONAL;

NONLINEAR EQUATIONS;

EID: 84891089489     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.J052635     Document Type: Article

References (32)

1. Kryloff N. and Bogoliuboff N. Introduction to Nonlinear Mechanics Princeton Univ. Press Princeton NJ 1947 pp. 8-54.
2. Gilmore R. J. and Steer M. B. "Nonlinear Circuit Analysis Using the Method of Harmonic Balance: A Review of the Art Part I. Introductory Concepts," International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering Vol. 1 No. 1 1991 pp. 22-37. doi:10.1002/(ISSN)1522- 6301
3. Nastov O. Spectral Methods for Circuit Analysis Ph.D. Thesis Massachusetts Inst. of Technology Cambridge MA 1999.
4. Kundert K. "Introduction to RF Simulation and Its Application," IEEE Journal of Solid-State Circuits Vol. 34 No. 9 1999 pp. 1298-1319. doi:10.1109/4.782091
5. Beran P. and Pettit C. "A Direct Method for Quantifying Limit-Cycle Oscillation Response Characteristics in the Presence of Uncertainties," AIAA Paper 2004-1695 April 2004.
6. Hall K. Thomas J. and Clark W. "Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique," AIAA Journal Vol. 40 No. 5 May 2002 pp. 879-886. doi:10.2514/3.15137
7. Gopinath A. and Jameson A. "Time Spectral Method for Periodic Unsteady Computations over Two-and Three-Dimensional Bodies," AIAA Paper 2005-1220 Jan. 2005.
8. McMullen M. The Application of Nonlinear Frequency Domain Methods to the Euler and Navier-Stokes Equations Ph.D. Thesis Stanford Univ. Stanford CA 2001.
9. McMullen M. Jameson A. and Alonso J. "Acceleration of Convergence to a Periodic Steady State in Turbomachineary Flows," AIAA Paper 2001-0152 2001.
10. LaBryer A. and Attar P. "High dimensional Harmonic Balance Dealiasing Techniques for a Duffing Oscillator," Journal of Sound and Vibration Vol. 324 No. 3 2009 pp. 1016-1038. doi:10.1016/j.jsv.2009.03.005
11. LaBryer A. and Attar P. "A Harmonic Balance Approach for Large-Scale Problems in Nonlinear Structural Dynamics," Computers and Structures Vol. 88 Nos. 17-18 2010 pp. 1002-1014. doi:10.1016/j.compstruc.2010.06.003
12. Maple R. King P. Orkwis P. and Wolff J. "Adaptive Harmonic Balance Method for Nonlinear Time-Periodic Flows," Journal of Computational Physics Vol. 193 No. 2 2004 pp. 620-641. doi:10.1016/j.jcp.2003.08.013
13. Thomas J. Custer C. Dowell E. and Hall K. "Unsteady Flow Computation Using a Harmonic Balance Approach Implemented about the OVERFLOW 2 Flow Solver," 19th AIAA Computational Fluid Dynamics Conference AIAA Paper 2009-4270 June 2009.
14. Blanc F. Roux F.-X. and Jouhaud J.-C. "Harmonic-Balance-Based Code-Coupling Algorithm for Aeroelastic Systems Subjected to Forced Excitation," AIAA Journal Vol. 48 No. 11 2010 pp. 2472-2481. doi:10.2514/1.45444
15. Maple R. King P.,Wolff J. and Orkwis P. "Split-Domain Harmonic Balance Solutions to Burger's Equation for Large-Amplitude Disturbances," AIAA Journal Vol. 41 No. 2 2003 pp. 206-212. doi:10.2514/2.1962
16. Sicot F. Puigt G. and Montagnac M. "Block-Jacobi Implicit Algorithms for the Time Spectral Method," AIAA Journal Vol. 46 No. 12 2008 pp. 3080-3089. doi:10.2514/1.36792
17. Dimitriadis G. "Continuation of Higher-Order Harmonic Balance Solutions for Nonlinear Aeroelastic Systems," Journal of Aircraft Vol. 45 No. 2 2008 pp. 523-537. doi:10.2514/1.30472
18. Kelley C. and Keyes D. "Convergence Analysis of Pseudo-Transient Continuation," SIAM Journal on Numerical Analysis Vol. 35 No. 2 1998 pp. 508-523. doi:10.1137/S0036142996304796
19. Liu L. Dowell E. and Hall K. "A Novel Harmonic Balance Analysis for the Van der Pol Oscillator," International Journal of Non-Linear Mechanics Vol. 42 No. 1 2007 pp. 2-12. doi:10.1016/j.ijnonlinmec.2006.09.004
20. Ekici K. and Hall K. "Nonlinear Frequency-Domain Analysis of Unsteady Flows in Turbomachinery with Multiple Excitation Frequencies," AIAA Journal Vol. 46 No. 8 2008 pp. 1912-1920. doi:10.2514/1.26006
21. Dai H.-H. Schnoor M. and Atluri S. "A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation and its Equivalence to the High Dimensional Harmonic Balance Method: Subharmonic Oscillations," Computer Modeling in Engineering and Sciences Vol. 84 No. 5 2012 pp. 459-497.
22. Mavriplis D. and Yang Z. "Time Spectral Method for Periodic and Quasi-Periodic Unsteady Computations on Unstructured Meshes," Mathematical Modelling of Natural Phenomena Vol. 6 No. 3 2011 pp. 213-236. doi:10.1051/mmnp/20116309
23. Lanczos C. Discourse on Fourier Series Vol. 3 Oliver & Boyd Edinburgh England U.K. 1966 pp. 1-255.
24. Gottlieb D. and Orszag S. Numerical analysis of spectral methods: theory and applications Vol. 26 Society for Industrial Mathematics 1987 pp. 71-77.
25. Sharrit D. "New Method of Analysis of Communication Systems," Presented at the IEEE MTT-S: Nonlinear Computer-Aided Design Workshop June 1996.
26. Feldmann P. and Roychowdhury J. "Computation of circuit Waveform Envelopes Using an Efficient Matrix-Decomposed Harmonic Balance Algorithm," 1996 IEEE/ACM International Conference on Computer-Aided Design (ICCAD-96): Digest of Technical Papers IEEE Publ. Piscataway NJ 1996 pp. 295-300.
27. Petzold L. "An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations," SIAM Journal on Numerical Analysis Vol. 18 No. 3 1981 pp. 455-479. doi:10.1137/0718030
28. Su X. and Yuan X. "Implicit Solution of Time Spectral Method for Periodic Unsteady Flows," International Journal for Numerical Methods in Fluids Vol. 63 No. 7 2010 pp. 860-876.
29. Titchmarsh E. The Theory of Functions Oxford Univ. Press London 1939 pp. 427-432.
30. Pokorný P. Schreiber I. and Marek M. "On the Route to Strangeness Without Chaos in the Quasiperiodically Forced Van der Pol Oscillator," Chaos Solitons & Fractals Vol. 7 No. 3 1996 pp. 409-424. doi:10.1016/0960-0779(95)00067-4
31. Xu J. and Jiang J. "The Global Bifurcation Characteristics of the Forced Van der Pol Oscillator," Chaos Solitons & Fractals Vol. 7 No. 1 1996 pp. 3-19. doi:10.1016/0960-0779(95)00045-3
32. MATLAB Software Package,Ver. 7.12.0.635 The MathWorks Natick MA 2011.